Dynamic nolinear Gauss-Helmert model and its robust total Kalman filter algorithm for GNSS-acoustic underwater positioning

doi:10.11947/j.AGCS.2023.20210467

Abstract

Abstract: The GNSS-acoustic combined observing is an important means to determine the position of seafloor control points, but it will be interfered by error factors such as the uncertainty in sound velocity and the positioning deviation of the sea surface platform. However, the processing strategy of general method based on the error propagation law for various errors makes the seafloor point coordinate solution inaccurate. To solve the above problems, this paper sets the time-invariant term of sound velocity ranging as the parameter to be solved, and discusses the influence of time-varying error of sound velocity ranging and transducer position error in the coefficient matrix of underwater observation equation. Thus, the dynamic nonlinear Gauss-Helmert (GH) model for GNSS-acoustic underwater positioning is constructed, and the total Kalman filter solution of this method is derived. On this basis, taking into account the gross errors polluting of the observations, the robust method and solution steps of the new model are given. Finally, simulation experiments and a testing experiment in the sea area near Jiaozhou Bay are used to verify the performance of the new model. The results show that under conditions with no gross errors and either different water depths or different transducer position errors, the accuracy and stability of the proposed method are both higher than those of the general method. When the observations are polluted by gross errors, the robust filter algorithm of the new model can accurately identify and locate the abnormal information. The precision of its 3D point deviation results can be obviously optimized, and the solution performance is superior to that of the general method.

Key words: GNSS-A technology, seafloor control point, sound velocity ranging error, nonlinear GH model, robust estimation

CLC Number:

P228

KUANG Yingcai, Lü Zhiping, LI Linyang, WANG Fangchao, XU Guochang. Dynamic nolinear Gauss-Helmert model and its robust total Kalman filter algorithm for GNSS-acoustic underwater positioning[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(4): 559-570.

References

[1] YANG Yuanxi, XU Tianhe, XUE Shuqiang. Progresses and prospects of marine geodetic datum and avigation in China[J]. Journal of Geodesy and Geoinformation Science, 2018(1): 16-24.
[2] 刘经南, 陈冠旭, 赵建虎, 等. 海洋时空基准网的进展与趋势[J]. 武汉大学学报(信息科学版),2019,44(1):20-40. LIU Jingnan, CHEN Guanxu, ZHAO Jianhu, et al. Development and trends of marine space-time frame network[J]. Geomatics and Information Science of Wuhan University, 2019, 44 (1): 17-37.
[3] SPIESS F N. Analysis of a possible sea floor strain measurement system[J]. Marine Geodesy, 1985, 9(4): 385-398.
[4] 曾安敏, 杨元喜, 明锋, 等. 海底大地基准点圆走航模式定位模型及分析[J]. 测绘学报, 2021, 50(7): 939-952. DOI: 10.11947/j.AGCS.2021.20200529. ZENG Anmin, YANG Yuanxi, MING Feng, et al. Positioning model and analysis of the sailing circle mode of seafloor geodetic datum points[J]. Acta Geodaetica et Cartographica Sinica, 2021, 50(7): 939-952. DOI: 10.11947/j.AGCS.2021.20200529.
[5] 孙文舟, 殷晓冬, 曾安敏, 等. 附加深度差和水平距离约束的深海控制点差分定位算法[J]. 测绘学报, 2019, 48(9): 1190-1196. DOI: 10.11947/j.AGCS.2019.20180514. SUN Wenzhou, YIN Xiaodong, ZENG Anmin, et al. Differential positioning algorithm for deep-sea control points on constraint of depth difference and horizontal distance constraint[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(9): 1190-1196. DOI: 10.11947/j.AGCS.2019.20180514
[6] 邝英才, 吕志平, 王方超, 等. GNSS/声学联合定位的自适应滤波算法[J]. 测绘学报, 2020, 49(7): 854-864. DOI: 10.11947/j.AGCS.2020.20190393. KUANG Yingcai, LÜ Zhiping, WANG Fangchao, et al. The adaptive filtering algorithm of GNSS/acoustic joint positioning[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(7): 854-864. DOI: 10.11947/j.AGCS.2020.20190393.
[7] YAMADA T, ANDO M, TADOKORO K, et al. Error evaluation in acoustic positioning of a single transponder for seafloor crustal deformation measurements[J].Earth, Planets and Space, 2002, 54(9): 871-881.
[8] FUJITA M, ISHIKAWA T, MOCHIZUKI M, et al. GPS/acoustic seafloor geodetic observation: method of data analysis and its application[J].Earth, Planets and Space, 2006, 58(3): 265-275.
[9] SPIESS F N, CHADWELL C D, HILDEBRAND J A, et al. Precise GPS/acoustic positioning of seafloor reference points for tectonic studies[J]. Physics of the Earth and Planetary Interiors, 1998, 108(2): 101-112.
[10] OSADA Y, FUJIMOTO H, MIURA S, et al. Estimation and correction for the effect of sound velocity variation on GPS/acoustic seafloor positioning: an experiment off Hawaii Island[J].Earth, Planets and Space, 2003, 55(10): e17-e20.
[11] SUN Wenzhou, YIN Xiaodong, ZENG Anmin. The relationship between propagation time and sound velocity profile for positioning seafloor reference points[J]. Marine Geodesy, 2019, 42(2): 186-200.
[12] XU Peiliang, ANDO M, TADOKORO K. Precise, three-dimensional seafloor geodetic deformation measurements using difference techniques[J].Earth, Planets and Space, 2005, 57(9): 795-808.
[13] ZHAO Jianhu, ZOU Yajing, ZHANG Hongmei, et al. A new method for absolute datum transfer in seafloor control network measurement[J].Journal of Marine Science and Technology, 2016, 21(2): 216-226.
[14] SUN Wenzhou, YIN Xiaodong, BAO Jingyang, et al. Semi-parametric adjustment model methods for positioning of seafloor control point[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(1): 85-92.
[15] ADCOCK R J. Note on the method of least squares[J]. The Analyst, 1877, 4(6): 183.
[16] FISHER G W, HUFFEL S V, VANDEWALLE J. The total least squares problem: computational aspects and analysis[J]. Mathematics of Computation, 1992, 59(200): 724.
[17] SCHAFFRIN B, WIESER A. On weighted total least-squares adjustment for linear regression[J]. Journal of Geodesy, 2008, 82(7): 415-421.
[18] NEITZEL F. Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation[J]. Journal of Geodesy, 2010, 84(12): 751-762.
[19] MAHBOUB V. On weighted total least-squares for geodetic transformations[J]. Journal of Geodesy, 2012, 86(5): 359-367.
[20] KUANG Yingcai, LU Zhiping, LI Linyang, et al. Robust constrained Kalman filter algorithm considering time registration for GNSS/acoustic joint positioning[J]. Applied Ocean Research, 2021, 107: 102435.
[21] CHADWELL C D. Shipboard towers for global positioning system antennas[J]. Ocean Engineering, 2003, 30(12): 1467-1487.
[22] 崔希璋,於宗俦,陶本藻,等. 广义测量平差[M]. 2版. 武汉:武汉大学出版社,2009. CUI Xizhang, YU Zongchou, TAO Benzao, et al. Generalized surveying adjustment[M]. 2nd ed. Wuhan: Wuhan University Press, 2009.
[23] FANG X. Weighted total least squares solutions for applications in geodesy[D]. Hannover: Leibniz University, 2011.
[24] 胡川,陈义. 非线性整体最小平差迭代算法[J]. 测绘学报,2014,43(7):668-674. HU Chuan, CHEN Yi. An iterative algorithm for nonlinear total least squares adjustment[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43 (7): 668-674.
[25] CHANG Guobin. On least-squares solution to 3D similarity transformation problem under Gauss-Helmert model[J]. Journal of Geodesy, 2015, 89(6): 573-576.
[26] 方兴,曾文宪,刘经南,等. 基于非线性高斯-赫尔默特模型的混合整体最小二乘估计[J]. 测绘学报,2016,45(3):291-296. DOI: 10.11947/j.AGCS.2016.20150157. FANG Xing, ZENG Wenxian, LIU Jingnan, et al. Mixed LS-TLS estimation based on nonlinear Gauss-Helmert model[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45 (3): 291-296. DOI: 10.11947/j.AGCS.2016.20150157.
[27] AMIRI-SIMKOOEI A, JAZAERI S. Weighted total least squares formulated by standard least squares theory[J]. Journal of Geodetic Science, 2012, 2(2): 113-124.
[28] SCHAFFRIN B, IZ H B. Towards total Kalman filtering for mobile mapping[C]//Proceedings of the 5th International Symposium on Mobile Mapping Technology. Padua, Italy: ISPRS, 2007, 270-275.
[29] MAHBOUB V, SAADATSERESHT M, ARDALAN A A. A general weighted total Kalman filter algorithm with numerical evaluation[J]. Studia Geophysica et Geodaetica, 2017, 61(1): 19-34.
[30] 余航, 王坚, 王乐洋, 等. 动态EIV模型及其总体卡尔曼滤波方法[J]. 测绘学报, 2018, 47(4): 480-489. DOI: 10.11947/j.AGCS.2018.20170098. YU Hang, WANG Jian, WANG Leyang, et al. Total Kalman filter method of dynamic EIV model[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(4): 480-489. DOI: 10.11947/j.AGCS.2018.20170098.
[31] 周江文. 经典误差理论与抗差估计[J]. 测绘学报, 1989, 18(2): 115-120. ZHOU Jiangwen. Classical theory of errors and robust estimation[J]. Acta Geodaetica et Cartographica Sinica, 1989, 18(2): 115-120.
[32] 王彬, 李建成, 高井祥, 等. 抗差加权整体最小二乘模型的牛顿-高斯算法[J]. 测绘学报, 2015, 44(6): 602-608. DOI: 10.11947/j.AGCS.2015.20130704. WANG Bin, LI Jiancheng, GAO Jingxiang, et al. Newton-Gauss algorithm of robust weighted total least squares model[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(6): 602-608. DOI: 10.11947/j.AGCS.2015.20130704.
[33] ROUSSEEUW P, LEROY A. Robust regression and outlier detection[M]. New York: John Wiley and Sons, 1987.
[34] YANG Y X. Robust estimation for dependent observations[J]. Manuscripta Geodaetica, 1994, 19: 10-17.
[35] CHADWELL C D, SWEENEY A D. Acoustic ray-trace equations for seafloor geodesy[J]. Marine Geodesy, 2010, 33(2/3): 164-186.
[36] MUNK W H. Sound channel in an exponentially stratified ocean, with application to SOFAR[J]. The Journal of the Acoustical Society of America, 1974, 55(2): 220-226.
[37] ZHAO Shuang, WANG Zhenjie, HE Kaifei, et al. Investigation on underwater positioning stochastic model based on acoustic ray incidence angle[J]. Applied Ocean Research, 2018, 77: 69-77.